Posts tagged 'v-v-prasolov'

GC-05.03 · Prasolov & Bùi Quang Tuân’s Equi-Area Irregular Pentagon

Let ABCDE be any convex pentagon—regular or irregular—whose five peripheral triangles \(\triangle ABE, \triangle ABC, \triangle BCD, \triangle CDE, \triangle DEA\) have equal area. Then every diagonal is parallel to the opposite side and is divided by the crossing diagonals in the golden ratio, e.g. \(|BM|/|MD| = \phi\).